The thing about a SLAP tear is that it doesn't get better without surgery, and recovery from that's a bitch.
With PT it has become manageable and I can do pushups with bands, pull-ups etc., but basically anything that puts pressure on the joint is going to cause pain (including sqauts, deadlifts, bench, dips etc.)
Still ways around it man. You can do lunges for leg stuff. What about hex bars for deads? Pull ups means that you can probably do pull downs and rows?
I'm guessing you're opposed to having surgery for the shoulder and are just going to make do with a more limited workout scheme?
The best advice I got post injury was to let pain be your guide. Try one new thing light in the gym every session and see how your body reacts. It took me a long time to find out what worked at the start when I'd get flare ups all the time.